All you need is LATE

Instrumental variable (IV) is a standard tool to measure the eect of a treatment. However, it relies on a strong “no-defiers” condition, and it captures the eect of the treatment for compliers only. This paper shows that “no-defiers” can be replaced by a weaker condition, which requires only that conditional on their treatment eects, more subjects move in the compliant direction than otherwise. This weaker condition is sucient to capture causal eects for a subgroup of same size as the standard population of compliers. It also shows that the eect of the treatment is the same for compliers as for a larger population G. As a result, IV also captures treatment eects for G. The size of G can be bounded. Those two results are used to reanalyze the internal and external validity of the estimates in Angrist & Evans (1998).

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